Sensitivity of reaction-diffusion manifolds (REDIM) method with respect to the gradient estimate

In this work, a mathematical formulation for the calculation of the sensitivity of manifold-based simplified chemistry with respect to the scalar gradient is derived. This methodology allows to answer how important the scalar gradient is for the Reaction-Diffusion Manifolds (REDIM) reduced chemistry and how sensitive the reduced scheme is with respect to the gradient estimate. Based on the governing REDIM evolution equation, the sensitivity equation is derived in form of a linear in-homogeneous partial differential equation system of second order with non-constant coefficients. Some examples including simple reaction systems and real combustion systems are shown to validate the approach. Moreover, the developed sensitivity analysis can also be used in other manifold-based methods.

Automated summary

In this study, a mathematical formulation for calculating the sensitivity of manifold-based simplified chemistry with respect to the scalar gradient was derived. The method provides insights into the importance of the scalar gradient in Reaction-Diffusion Manifolds (REDIM) chemistry and the sensitivity of the reduced scheme to the gradient estimate. The approach was validated using examples of simple reaction systems and real combustion systems. The developed sensitivity analysis can also be applied to other manifold-based methods.